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Teorema da esfera suave via fluxo de Ricci
(Universidade Federal de São Carlos, 2023-08-04)
The goal of this dissertation is the theoretical development of the Ricci flow, a differential equation over a family of Riemannian metrics on an arbitrary differentiable manifold, and its use in the proof of the so-called ...
On the classification of two dimensional flows
(Universidade Federal de São Carlos, 2023-08-02)
Lawrence Markus, a well-known mathematician, published, in 1954, a strong result about classification of planar vector fields. Afterwards, Dean Arnold Neumann generalized such work for continuous flows, and the result ...
Campos de Yang-Mills fracamente estáveis na esfera de dimensão quatro
(Universidade Federal de São Carlos, 2023-05-03)
In this work we made a quick study on some basic results related to Groups and Lie Algebras,
action of Groups and Fiber Bundles with the objective of defining connections in Principal Bundles
and, later, in Associated ...
Merge trees decoradas e TDA
(Universidade Federal de São Carlos, 2023-08-10)
In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of ...
Attractors for processes on time-dependent spaces
(Universidade Federal de São Carlos, 2022-04-12)
The goal of this master’s degree dissertation is to study the asymptotic behavior of non-autonomous
hyperbolic partial differential equations with time-dependent coefficients. In order to achieve that, we
introduce the ...
Algumas aplicações de p-pontos
(Universidade Federal de São Carlos, 2023-08-24)
In this work we analyze the concept of \(p\)-points in \(\omega\) and its relation with forcing, in particular Sacks forcing and side-by-side Sacks forcing. With this we verify that the existence of \(p\)-points with ...
Existência global para a equação periódica e dispersiva de Hunter-Saxton
(Universidade Federal de São Carlos, 2021-03-15)
In this master's thesis, we study the recent results about global existence for the integrable dispersive Hunter–Saxton equation in a periodic domain. Firstly, the local well-posedness of the Cauchy problem of the equation ...
Um princípio de tangência e aplicações
(Universidade Federal de São Carlos, 2021-12-17)
We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which ...
Categoria de Lusternik-Schnirelmann e aplicações
(Universidade Federal de São Carlos, 2022-02-14)
The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ...
Um estudo de valorizações transcendentes e algébricas via polinômios-chaves e pares minimais
(Universidade Federal de São Carlos, 2022-02-24)
The main goal of this work is to study transcendental valuations and algebraic valuations. To achieve this, we use some of the main objects in Valuation Theory, such as key polynomials, truncations and minimal pairs. These ...